# Z-test for proportions

August 3, 2010 Leave a comment

Follow these steps to calculate a Z-test for proportions (see if proportional changes are significant across two samples)

### First, Calculate p̂

p̂ = Total number of units in the two samples that you want to look at (e.g. OCTUs in a subset of interest)

Total number of units in the two samples (e.g. total number of OCTUs)

### Next, you need to calculate (an estimate of) Standard Deviation :

σ p̂₁ – p̂₂ = √(p̂(1 – p̂) (1/n ₁ +(1/n₂)

σ stands for an estimate

### Finally, you can conduct a Z test for proportions:

Z = (p̂ ₁- p̂ ₂)

σ p̂₁ – p̂₂

A P value < 0.01 is equivalent to a Z-score > |2.575|

A P value <0.05 is equivalent to a Z-score > |1.96|

### Defining Well-sampled OCTUs:

# Minimum number of reads in a well-sampled OCTU = (3*STDEV)/(SQRT(#OCTUS))